Freudenthal, Hans 19051990
Overview
Works:  243 works in 853 publications in 9 languages and 10,944 library holdings 

Genres:  Popular works Conference papers and proceedings Biography Abstracts 
Roles:  Author, Editor, Organizer of meeting, Recipient, Other, Correspondent, Honoree, Translator, Contributor 
Classifications:  QA11, 510.7 
Publication Timeline
.
Most widely held works about
Hans Freudenthal
 All positive action starts with criticism : Hans Freudenthal and the didactics of mathematics by Sacha la Bastidevan Gemert( )
 Schrijf dat op, Hans : knipsels uit een leven by Hans Freudenthal( Book )
 HF : working on mathematics education by Fred Goffree( Book )
 Zeven grondleggers van de onderwijskunde : B. Brugsma, Ph. J. Idenburg, . Freudenthal, F.W. Prins, J.W. van Hulst, L. van Gelder en C.F. van Parreren( Book )
 "Elke positieve actie begint met critiek" : Hans Freudenthal en de didactiek van de wiskunde by Sacha la Bastidevan Gemert( Book )
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fewer
Most widely held works by
Hans Freudenthal
Didactical phenomenology of mathematical structures by
Hans Freudenthal(
)
34 editions published between 1983 and 2005 in English and held by 1,320 WorldCat member libraries worldwide
The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the ‘ground’ which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOOK BACKWARD AND A LOOK FORWARD Men die, systems last
34 editions published between 1983 and 2005 in English and held by 1,320 WorldCat member libraries worldwide
The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the ‘ground’ which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOOK BACKWARD AND A LOOK FORWARD Men die, systems last
Revisiting mathematics education : China lectures by
Hans Freudenthal(
)
34 editions published between 1991 and 2010 in 3 languages and held by 1,200 WorldCat member libraries worldwide
This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in mathematics education. The book is divided into three chapters. Chapter 1, "Mathematics Phenomenologically", explores different aspects of mathematics: What is Mathematics?; "Didactical Principles", discusses the organization of the teaching/learning processes relevant to mathematics, and is divided into four subsections: (1) Guided Reinvention; (2) Bonds with Reality; (3) Learning Processes; and (4) Longterm Learning Processes. Finally, chapter 3, "The Landscape of Mathematics Education", explores the theoretical foundations of mathematics education, and relates it to the current research and practice in the fields in three subsections: (1) Theory of Mathematics Education; (2) Research in Mathematics Education; and (3) Practice of Mathematics Education. Included is a list of the author's publications on mathematics education containing 201 entries. (Mdh)
34 editions published between 1991 and 2010 in 3 languages and held by 1,200 WorldCat member libraries worldwide
This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in mathematics education. The book is divided into three chapters. Chapter 1, "Mathematics Phenomenologically", explores different aspects of mathematics: What is Mathematics?; "Didactical Principles", discusses the organization of the teaching/learning processes relevant to mathematics, and is divided into four subsections: (1) Guided Reinvention; (2) Bonds with Reality; (3) Learning Processes; and (4) Longterm Learning Processes. Finally, chapter 3, "The Landscape of Mathematics Education", explores the theoretical foundations of mathematics education, and relates it to the current research and practice in the fields in three subsections: (1) Theory of Mathematics Education; (2) Research in Mathematics Education; and (3) Practice of Mathematics Education. Included is a list of the author's publications on mathematics education containing 201 entries. (Mdh)
Weeding and sowing : preface to a science of mathematical education by
Hans Freudenthal(
)
32 editions published between 1978 and 2004 in English and held by 996 WorldCat member libraries worldwide
A title that sounds like poetry, and a subtitle that seems to contradict the title! But the subtitle is right, and originally it was just the title. A strange subtitle, isn’t it? Preface to a Science of Mathematical Education. All sciences – in their prenatal stage – have known this kind of literature: only the term used was not ‘Preface’, but, for instance, ‘Prolegomena’, which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the first results comes modesty. This is the preface to a book that will never be written: not by me, nor by anybody else. Once a science of mathematical education exists, it will get the preface it deserves. Nevertheless this preface – or what for honesty’s sake I have labelled so – must fulfil a function: the function of accelerating the birth of a science of mathematical education, which is seriously impeded by the unfounded view that such already exists. Against this view I have to argue: it rests on a wrong estimation – both over and under estimation at the same time – of what is to be considered as science
32 editions published between 1978 and 2004 in English and held by 996 WorldCat member libraries worldwide
A title that sounds like poetry, and a subtitle that seems to contradict the title! But the subtitle is right, and originally it was just the title. A strange subtitle, isn’t it? Preface to a Science of Mathematical Education. All sciences – in their prenatal stage – have known this kind of literature: only the term used was not ‘Preface’, but, for instance, ‘Prolegomena’, which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the first results comes modesty. This is the preface to a book that will never be written: not by me, nor by anybody else. Once a science of mathematical education exists, it will get the preface it deserves. Nevertheless this preface – or what for honesty’s sake I have labelled so – must fulfil a function: the function of accelerating the birth of a science of mathematical education, which is seriously impeded by the unfounded view that such already exists. Against this view I have to argue: it rests on a wrong estimation – both over and under estimation at the same time – of what is to be considered as science
The language of logic by
Hans Freudenthal(
Book
)
62 editions published between 1961 and 1975 in 6 languages and held by 924 WorldCat member libraries worldwide
62 editions published between 1961 and 1975 in 6 languages and held by 924 WorldCat member libraries worldwide
Probability and statistics by
Hans Freudenthal(
Book
)
52 editions published between 1957 and 1981 in 6 languages and held by 764 WorldCat member libraries worldwide
52 editions published between 1957 and 1981 in 6 languages and held by 764 WorldCat member libraries worldwide
Linear lie groups by
Hans Freudenthal(
Book
)
23 editions published between 1969 and 1979 in 3 languages and held by 726 WorldCat member libraries worldwide
23 editions published between 1969 and 1979 in 3 languages and held by 726 WorldCat member libraries worldwide
The Concept and the role of the model in mathematics and natural and social sciences proceedings of the colloquium sponsored
by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences organized at Utrecht,
January 1960 by
Hans Freudenthal(
Book
)
26 editions published in 1961 in English and German and held by 552 WorldCat member libraries worldwide
26 editions published in 1961 in English and German and held by 552 WorldCat member libraries worldwide
Mathematics as an educational task by
Hans Freudenthal(
Book
)
21 editions published between 1972 and 1973 in English and Undetermined and held by 546 WorldCat member libraries worldwide
Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thoughtexperiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno's slave. The thoughtexperi ment tries to find out how a student could reinvent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book
21 editions published between 1972 and 1973 in English and Undetermined and held by 546 WorldCat member libraries worldwide
Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thoughtexperiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno's slave. The thoughtexperi ment tries to find out how a student could reinvent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book
Mathematics observed by
Hans Freudenthal(
Book
)
14 editions published between 1967 and 1970 in 3 languages and held by 523 WorldCat member libraries worldwide
14 editions published between 1967 and 1970 in 3 languages and held by 523 WorldCat member libraries worldwide
Lincos; design of a language for cosmic intercourse by
Hans Freudenthal(
Book
)
19 editions published in 1960 in English and Dutch and held by 439 WorldCat member libraries worldwide
19 editions published in 1960 in English and Dutch and held by 439 WorldCat member libraries worldwide
Algebraical and topological foundations of geometry; proceedings by
Hans Freudenthal(
Book
)
17 editions published between 1959 and 2015 in English and German and held by 427 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications
17 editions published between 1959 and 2015 in English and German and held by 427 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications
Mathematik als pädagogische Aufgabe by
Hans Freudenthal(
Book
)
30 editions published between 1973 and 1979 in German and held by 248 WorldCat member libraries worldwide
30 editions published between 1973 and 1979 in German and held by 248 WorldCat member libraries worldwide
Logique mathematique appliquee by
Hans Freudenthal(
Book
)
14 editions published in 1958 in French and English and held by 193 WorldCat member libraries worldwide
14 editions published in 1958 in French and English and held by 193 WorldCat member libraries worldwide
Raumtheorie by
Hans Freudenthal(
Book
)
10 editions published in 1978 in German and held by 135 WorldCat member libraries worldwide
10 editions published in 1978 in German and held by 135 WorldCat member libraries worldwide
The Legacy of Hans Freudenthal by
Leen Streefland(
Book
)
8 editions published in 1993 in English and held by 129 WorldCat member libraries worldwide
"The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or coworkers. They testify to what they learned from him. Freudenthal himself contributes posthumously. His didactical phenomenology of the concept of force is both provocative and revealing in its originality, compared with what is usually found in physics instruction."BOOK JACKET. "Freudenthal is portrayed as a universal human being by Josette Adda. He made considerable contributions to mathematics itself, e.g. on Homotopy Theory and Lie Groups in Geometry. The exposition of Freudenthal's mathematical life and work is on Van Est's account."BOOK JACKET. "Henk Bos discusses his historical work. The essay review of the 8th edition of Hilbert's Grundlagen der Geometrie serves as a vehicle of thought."BOOK JACKET. "The main part of the book, however, concerns Freudenthal's work on Mathematics Education. Christine Keitel reviews his final book Revisiting Mathematics Education (1991). Fred Goffree describes Freudenthal's 'Working on mathematics education' both from a historical as well as a theoretical perspective. Adrian Treffers analyses Freudenthal's influence on the development of realistic mathematics education at primary level in the Netherlands, especially his influence on the Wiskobasproject of the former IOWO. Freudenthal once predicted the disappearance of mathematics as an individual subject in education sometime around the year 2000, because it would by then have merged with integrated thematic contexts. Jan de Lange anticipates this future development and shows that Freudenthal's prediction will not come true after all. Reflective interludes unveil how he might have influenced those developments. Freudenthal contributed a wealth of ideas and conceptual tools to the development of mathematics education, e.g. on contexts, didactical phenomenology, guided reinvention, mathematisation, the constitution of mental objects, the development of reflective thinking, levels in learning processes, the development of a mathematical attitude and so on, but he did not design very much concrete material. Leen Streefland is dealing with the question of design from a theoretical point of view, while applying Freudenthal's ideas on changing perspective and shifting."BOOK JACKET. "This is a nutshell reflects the richness of the content of this volume that is of interest to teachers, researchers, mathematics educators, mathematicians, educationalists, psychologists and policy makers."BOOK JACKET
8 editions published in 1993 in English and held by 129 WorldCat member libraries worldwide
"The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or coworkers. They testify to what they learned from him. Freudenthal himself contributes posthumously. His didactical phenomenology of the concept of force is both provocative and revealing in its originality, compared with what is usually found in physics instruction."BOOK JACKET. "Freudenthal is portrayed as a universal human being by Josette Adda. He made considerable contributions to mathematics itself, e.g. on Homotopy Theory and Lie Groups in Geometry. The exposition of Freudenthal's mathematical life and work is on Van Est's account."BOOK JACKET. "Henk Bos discusses his historical work. The essay review of the 8th edition of Hilbert's Grundlagen der Geometrie serves as a vehicle of thought."BOOK JACKET. "The main part of the book, however, concerns Freudenthal's work on Mathematics Education. Christine Keitel reviews his final book Revisiting Mathematics Education (1991). Fred Goffree describes Freudenthal's 'Working on mathematics education' both from a historical as well as a theoretical perspective. Adrian Treffers analyses Freudenthal's influence on the development of realistic mathematics education at primary level in the Netherlands, especially his influence on the Wiskobasproject of the former IOWO. Freudenthal once predicted the disappearance of mathematics as an individual subject in education sometime around the year 2000, because it would by then have merged with integrated thematic contexts. Jan de Lange anticipates this future development and shows that Freudenthal's prediction will not come true after all. Reflective interludes unveil how he might have influenced those developments. Freudenthal contributed a wealth of ideas and conceptual tools to the development of mathematics education, e.g. on contexts, didactical phenomenology, guided reinvention, mathematisation, the constitution of mental objects, the development of reflective thinking, levels in learning processes, the development of a mathematical attitude and so on, but he did not design very much concrete material. Leen Streefland is dealing with the question of design from a theoretical point of view, while applying Freudenthal's ideas on changing perspective and shifting."BOOK JACKET. "This is a nutshell reflects the richness of the content of this volume that is of interest to teachers, researchers, mathematics educators, mathematicians, educationalists, psychologists and policy makers."BOOK JACKET
Selecta by
Hans Freudenthal(
Book
)
9 editions published in 2009 in German and English and held by 103 WorldCat member libraries worldwide
Hans Freudenthal (1905  1990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics
9 editions published in 2009 in German and English and held by 103 WorldCat member libraries worldwide
Hans Freudenthal (1905  1990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics
Lie groups by
Hans Freudenthal(
Book
)
14 editions published between 1960 and 1961 in English and Undetermined and held by 85 WorldCat member libraries worldwide
14 editions published between 1960 and 1961 in English and Undetermined and held by 85 WorldCat member libraries worldwide
Vorrede zu einer Wissenschaft vom Mathematikunterricht by
Hans Freudenthal(
Book
)
5 editions published in 1978 in German and held by 83 WorldCat member libraries worldwide
5 editions published in 1978 in German and held by 83 WorldCat member libraries worldwide
Mathematik in Wissenschaft und Alltag by
Hans Freudenthal(
Book
)
10 editions published between 1968 and 1977 in German and Russian and held by 76 WorldCat member libraries worldwide
10 editions published between 1968 and 1977 in German and Russian and held by 76 WorldCat member libraries worldwide
Collected works by
L. E. J Brouwer(
Book
)
11 editions published between 1975 and 1976 in English and Multiple languages and held by 61 WorldCat member libraries worldwide
11 editions published between 1975 and 1976 in English and Multiple languages and held by 61 WorldCat member libraries worldwide
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Related Identities
 Vries, H. de (Hendrik) 1932
 International Union of the History and Philosophy of Science Division of Philosophy of Sciences
 International Mathematical Union Other
 Bastidevan Gemert, Sacha la Author
 Vincken, Marianne Translator
 Third, William Translator
 Brouwer, L. E. J. (Luitzen Egbertus Jan) 18811966 Author
 Streefland, Leen 1939 Other Author
 Springer, T. A. (Tonny Albert) 1926 Editor
 Dalen, D. van (Dirk) 1932 Editor
Useful Links
Associated Subjects
Algebraic topology College teachers Continuous groups Education Educators Electromechanical analogies Freudenthal, Hans, Geometry Geometry, Differential GeometryFoundations Group actions (Mathematics) Group theory Homotopy theory Humanities Intuitionistic mathematics Lie algebras Lie groups Lincos (Artificial language) Logic, Symbolic and mathematical Mathematical models Mathematicians Mathematics MathematicsPhilosophy MathematicsStudy and teaching MathematicsStudy and teachingAudiovisual aids MathematicsStudy and teachingPhilosophy Netherlands NetherlandsUtrecht Parreren, Carel Frederik van Probabilities Science ScienceMethodology SciencePhilosophy Statistics Topological groups Topology
Covers
Alternative Names
Freidental, Kh.
Freĭdentalʹ, Kh 19051990
Freĭdentalʹ, Kh. (Khans), 19051990
Freidental, Khans.
Freĭdentalʹ, Khans 19051990
Frejdentalʹ, Ch
Frejdentalʹ, Ch 19051990
Frejdental', Gans.
Frejdental', Gans 19051990
Frejdental', H.
Freudenthal, H.
Freudenthal, H. 19051990
Freudenthal, Hans
Freudenthal, Hans, 1905
Frojdental', G.
Frojdental', G. 19051990
Frojdental', Gans.
Frojdental', Gans 19051990
Hans Freudenthal deutscher Mathematiker
Hans Freudenthal Dutch mathematician
Hans Freudenthal matemàtic neerlandès
Hans Freudenthal matematician olandez
Hans Freudenthal matemático neerlandés
Hans Freudenthal matematico tedesco
Hans Freudenthal mathématicien allemand
Hans Freudenthal tysk professor
Sirlof, V. 19051990
Sirolf, V. 19051990
Фрейденталь, Ганс 19051990
Фрейденталь, Х.
Фрейденталь, Ханс
Фройденталь, Ханс
Ханс Фройдэнталь
הנס פרוידנטל
הנס פרוידנטל מתמטיקאי הולנדי
هانس فرودنثال رياضياتي ألماني
프로이덴탈, 한스 19051990
한스 프로이덴탈
ハンス・フロイデンタール
フロイデンタール, H
汉斯·弗洛伊登萨
漢斯·弗賴登塔爾得
Languages